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Analysis of the temperature behavior model for the
optimization of sowing (TOMATO (Solanum
licopersicum))
Análisis del modelo de comportamiento de las temperaturas
para la optimización de la siembra (TOMATE) (Solanum
licopersicum)
Submitted (24.07.2020) - Accepted (02.12.2020)
ABSTRACT
Mathematics has continued to increase its presence in the sciences
and in the economic sectors, in general. Along with information
technologies, huge volumes of data are processed that facilitate
analysis and serve for objective decision-making. The avoidance of
agricultural risks is a task of the first order to safeguard food
security and thus reducing the vegetative periods in crops is an
effective strategy to achieve it. The work is carried out in the
Babahoyo canton, Los Ríos province on obtaining behavior models
of air temperatures that facilitate, through the application of
Differential Calculation, obtaining the dates of maximum
temperatures, which would allow obtaining the periods of higher
temperatures. thermal supply to accelerate growth and
development processes. The dates of maximum temperature were
located around decade 7, between March 13 and 17, results of the
sum of probabilities for 75%. The sums of temperatures obtained
fluctuate in the range 2170 – 2266 Celsius Degrees that guarantee
the acceleration of the vegetative period, since they have 100% of
the sum of probabilities of being reached. Observe a management
directed to the selection of the period of highest temperature will
reduce the risks of pests and extreme events, in addition to
reducing inputs in agricultural production, which will increase the
sustainability of the system.
Keywords: Temperatures, Modeling, Optimization, Tomato.
Leonardo Santiago Vinces Llaguno
Student of the Academic Master's Degree
with Mathematical Research Trajectory,
Graduate Institute, Universidad Técnica de
Manabí, Portoviejo (Ecuador)
lvinces0182@utm.edu.ec,
https://orcid.org/0000-0002-9888-4646
Yaima Trujillo Reyes
Bachelor's Degree in Mathematics, Master's
Degree in Applied Mathematics, Faculty of
Agricultural Sciences, Universidad Técnica
Estatal de Quevedo, Los Ríos (Ecuador)
ytrujillo@uteq.edu.ec
https://orcid.org/0000-0001-7357-0707
Revista Científica Interdisciplinaria
Investigación y Saberes
Vol. - 11 No. 2
May - August 2021
e-ISSN: 1390-8146
1-10
2
Leonardo Santiago Vinces Llaguno
Yaima Trujillo Reyes
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
RESUMEN
Las matemáticas han seguido elevando su presencia en las ciencias y en los sectores
económicos, en general. Junto a las tecnologías de la información se procesan enormes
volúmenes de datos que facilitan el análisis y sirven para la toma de decisiones de manera
objetiva. La evasión de los riesgos agrícolas resulta una tarea de primer orden para la
salvaguarda de la seguridad alimentaria y es así que la reducción de los períodos
vegetativos en los cultivos, resulta una estrategia eficaz para lograrlo. El objetivo de este
trabajo es determinar las fechas en que se producen las máximas de temperatura del aire
para obtener los períodos probables en que se manifiestan los valores más altos y acelerar
el crecimiento y desarrollo del cultivo del tomate en el cantón Babahoyo, provincia Los
Ríos, Ecuador. Las fechas de máxima temperatura en el aire se ubicó alrededor de la
decena 7, entre el 13 y el 17 de marzo, resultados de la suma de probabilidades para un
75%. Las sumas de temperaturas obtenidas fluctúan en el rango 2170 – 2266 Grados
Celsius que garantizan la aceleración del período vegetativo, pues cuentan con el 100%
de la suma de probabilidades de ser alcanzadas. Observar un manejo dirigido a la
selección del período de mayor temperatura reducirá los riesgos de y eventos extremos,
además de disminuir los insumos en la producción agrícola, lo que aumentará la
sostenibilidad del sistema.
Palabras clave: Temperaturas, Modelación, Optimización, Tomate.
1. Introduction
The need to increase agricultural production worldwide has determined the
introduction of modeling and advanced statistical-mathematical tools in research
(Rodriguez, 2001). The adequate use and interpretation of these techniques allow
optimal decision making, efficiency and the achievement of superior efforts in
different spheres, especially in the agricultural sector, whose application favors
the development of productive systems (Rodríguez & Bermúdez, 1995; Chávez et
al., 2013). As reported (Chávez et al., 2013), in order to make medium and long-
term decisions under similar experimental conditions, applied mathematics in
agricultural sciences provides criteria and basic tools to better manage and
interpret agricultural activity and meet the demands of new technologies to
produce in highly competitive global markets while safeguarding natural
resources.
Agricultural productivity is an important component of the global carbon cycle
and a driver of the most essential ecosystem services for humanity (Vitousek et
al.,1986; Costanza et al.,1998). Research on agricultural productivity has attracted
much attention among the scientific community because it is an indicator of
energy input to the biosphere and a measure of net assimilation of carbon dioxide
(
CO2
) providing a basis for assessing the status of a wide range of ecological
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
processes (Pan et al., 2014). The behavior of maximum temperature plays a very
active role in this whole process.
Many authors have shown that there is a close relationship between changes in
agricultural productivity and the behavior of climatic variables (Tiedemann, 2015;
Deliree et al. , 2018; Pan et al., 2015). A higher correlation was found between
agricultural productivity and temperature than that found with precipitation,
concluding that these changes are closely related to climatic factors, landscape
conditions and vegetation type (Yang et al., 2020). Other authors have related it
to the length of the growing season (Arora & Boer, 2005; Jönsson & Eklundh,
2004; Chandola et al. , 2010).
The projected increase in global average temperature of 4.3 ± 0.7 degrees Celsius
by 2100 will affect the geographic distribution, composition and productivity of
tropical ecosystems (Elikana et al., 2020), a change that is currently taking place
gradually. Therefore, management that guarantees the efficient use of ecosystem
resources is necessary. Thus, crops depend on a certain amount of temperature
sum for their growth and development, where the average must exceed a
biological minimum (De Fina & Ravelo, 1979). Causing crops to pass through
favorable climatic conditions that determine rapid growth and development
reduces the risk of pest attack, in addition to increasing the productive efficiency
of the system. On the other hand, there are cyclical phenomena (sequence of
ordered states that are repeated without alteration of the order) such as the
behavior of daily, monthly or annual temperature. These cyclical phenomena are
mathematically associated with periodic functions (Plaza, 2011).
Materials and methods
The present work was developed in the Babahoyo canton, Los Ríos province, to
determine the period in which the highest temperature values are reached
through its behavioral model. Thirty years of decennial mean temperature data
for the period 1981 - 2010 were used and in each of the years the behavioral
model and the value of the existing correlations were determined through the
application of SPSS software, the Curve Expert, an important element for the
selection of the model that best explained the results. The tomato variety selected
has a vegetative cycle equivalent to 180 days and a minimum biological
temperature equal to 13 degrees Celsius.
Once the functions were obtained for each curve in each year, the function was
optimized to obtain the maximum temperature through differential calculus:
derivative of the function equal to zero, to obtain the extreme values, from which
4
Leonardo Santiago Vinces Llaguno
Yaima Trujillo Reyes
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
the absolute maximum is acquired. For the development of this section, the
methodology proposed by (Morales, 1993) was used, which is based on the use
of differential calculus for the optimization of the functions in question. Once the
absolute maximum was obtained, it was possible to determine the periods of
greatest accumulation of heat summation, taking as the midpoint the date on
which the absolute maximum occurred and extending to the right and left the
same period of time, until it coincided with the length of the growth period of the
crop in question (Figure 1).
Figure 1. Temperature behavior during the growing period of the crop.
Source: Authors' own elaboration.
Once the optimum periods for each of the years and the average temperatures
corresponding to each of the tens involved in the growing period of the tomato
crop have been obtained, the cumulative probability in dates of maximum
temperature manifestation is evaluated for a 75% probability. The 75%
guarantees that out of every 10 years, the phenomenon occurs in 7.5 years, which
represents a lower risk for the farmer (Eldin & Rojas, 1983).
The sum of accumulated temperatures in each of the years was calculated. The
sum of probabilities of the sums of effective temperatures was evaluated.
𝑆𝑇
!
= 𝑛(𝑇
"
− 𝑇
"#
)
STe - sum of effective temperatures
n - number of days
Tm - average temperature
Tmb - minimum biological temperature
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
3. Results
Among the models analyzed, the best fit models were the sinusoidal and the
polynomial, in that order. The best fitting model has the form of a cosine wave:
𝑇 = 𝐴. cos
(
𝐵𝑡 + 𝐶
)
+ 𝐷
The above results coincide with those obtained by (Plaza, 2011) in his work on
daily temperature modeling in Valle del Cauca, Colombia.
From the annual temperature behavior models and with the application of the
differential calculation, the maximums for each year were obtained. In general,
the behavior of the temperature is cyclical, with a maximum that fluctuated
around the 7th decade and a minimum that fluctuated around the 21st and 22nd
decades. If the decades are taken to a decimal scale, then the maximum
fluctuated in the range 6.76 - 7.88, which converted to exact dates would be
8/March - 19/March. This method ensures that the periods when the highest
temperatures occur in each year are evaluated.
Table 1 presents for each year the equations of the behavior models of the
decennial temperature, correlation coefficients (Coef. Correl.), standard error
(SE), the tens of manifestation of the maximums and their corresponding dates,
which also presents the dates 90 days before (F.BEFORE) and 90 days after
(F.AFTER) the date of maximum, so as to include the tomato growth period, which
has a duration of 180 days. The characteristic of these functions is that their values
are repeated at regular intervals and their periodicity, as asserted by (San Martín,
2005).
Table 1. Models of annual temperature behavior, statisticians, dates of
manifestation of maximums and optimum development period for tomato
cultivation.
ECUATION
Coef.
Correl.
EN
TENS
F.BEFORE
DATE
F.AFTER
y=24.64+1.41 cos (0.17x-1.30)
0.91
0.45
7.29
8/12
13/3
11/6
y=24.61+1.37 cos (0.17x-1.28)
0.91
0.46
7.53
10/12
15/3
13/6
y=24.58+1.39 cos (0.17x-1.28)
0.92
0.44
7.53
10/12
15/3
13/6
y=24.58+1.42 cos (0.17x-1.26)
0.93
0.39
7.41
9/12
14/3
12/6
y=24.65+1.44 cos (0.17x-1.20)
0.94
0.36
7.06
6/12
11/3
9/6
y=24.65+1.36 cos (0.17x-1.21)
0.92
0.40
7.12
6/12
11/3
9/6
y=24.55+1.24 cos (0.17x-1.34)
0.89
0.45
7.88
14/12
19/3
17/6
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Leonardo Santiago Vinces Llaguno
Yaima Trujillo Reyes
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
y=24.65+1.43 cos (0.16x-1.19
0.92
0.43
7.44
9/12
14/3
12/6
y=24.58+1.46 cos (0.18x-1.40)
0.93
0.40
7.78
13/12
18/3
16/6
y=24.67+1.35 cos (0.17x-1.25)
0.92
0.40
7.35
9/12
14/3
12/6
y=24.61+1.42 cos (0.18x-1.40)
0.92
0.43
7.78
13/12
18/3
16/6
y=24.56+1.46 cos (0.17x-1.28)
0.93
0.42
7.53
10/12
15/3
13/6
y=24.71+1.32 cos (0.16x-1.17)
0.91
0.44
7.31
8/12
13/3
11/6
y=24.56+1.43 cos (0.18x-1.38)
0.91
0.45
7.67
12/12
17/3
15/6
y=24.65+1.37 cos (0.17x-1.29)
0.92
0.42
7.59
11/12
16/3
14/6
y=24.59+1.43 cos (0.17x-1.22)
0.90
0.50
7.18
7/12
12/3
10/6
y=24.64+1.45 cos (0.17x-1.25)
0.91
0.47
7.35
9/12
14/3
12/6
y=24.61+1.37 cos (0.17x-1.29)
0.91
0.43
7.59
11/12
16/3
14/6
y=24.61+1.43 cos (0.17x-1.34)
0.92
0.43
7.88
14/12
19/3
17/6
y=24.54+1.39 cos (0.18x-1.35)
0.92
0.41
7.50
10/12
15/3
13/6
y=24.63+1.46 cos (0.17x-1.34)
0.92
0.45
7.88
14/12
19/3
17/6
y=24.62+1.41 cos (0.17x-1.19)
0.92
0.44
7.00
5/12
10/3
8/6
y=24.66+1.35 cos (0.17x-1.15)
0.91
0.45
6.76
3/12
8/3
6/6
y=24.64+1.36 cos (0.18x-1.41)
0.92
0.41
7.83
13/12
18/3
16/6
y=24.56+1.43 cos (0.18x-1.39)
0.94
0.38
7.72
12/12
17/3
15/6
y=24.64+1.41 cos (0.17x-1.24)
0.92
0.44
7.29
8/12
13/3
11/6
y=24.57+1.35 cos (0.17x-1.27)
0.93
0.39
7.47
10/12
15/3
13/6
y=24.60+1.41 cos (0.17x-1.33)
0.92
0.43
7.82
13/12
18/3
16/6
y=24.63+1.43 cos (0.17x-1.34)
0.91
0.46
7.88
14/12
19/3
17/6
y=24.58+1.34 cos (0.17x-1.28)
0.91
0.44
7.53
10/12
15/3
13/6
The evaluation of the sum of probabilities shows that there is a 75% probability
that the maximum temperature will occur before March 17 and after March 13
(Figure 2).
Figure 2. Sum of probabilities of the dates of manifestation of the maximum
temperature before and after in Babahoyo canton, Los Ríos province. Source:
Authors' own elaboration.
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
The sum of effective temperatures for the selected periods, according to the
methodological procedure, fluctuated in the range 2170-2266
oC
. The sum of
effective temperatures for tomato fluctuates between 1150 and 1350 degrees
Celsius (De Fina, 1979) and according to the results, the temperature sums
obtained in the canton can determine a reduction of one third of the vegetative
period of the crop until harvest, with the implications that this has on inputs and
risks of pests and extreme events. The temperature sums in the canton exceed
the 1350
oC
required by the crop at the lowest value (Figure 3).
Figure 3. Sum of probabilities of the sum of effective temperatures in the tomato
crop in the periods of highest temperature in Babahoyo canton, Los Ríos province.
Source: Authors' own elaboration.
5. Conclusions
The model with the best fit was the sinusoidal model due to the cyclical and
periodic nature of the annual temperatures. The correlation coefficients were
high, although with direct observation models in each of the years, the
adjustments obtained could be somewhat improved. The use of differential
calculus to determine the dates of maximum temperature was of great support
to achieve the objective of this work, providing an applicable model for the
forecast of the periods with the highest thermal supply in the Babahoyo canton.
The sum of probabilities of the date of manifestation of maximum temperatures
presents a small variation in the range, which corresponds to the behavior of the
thermal conditions present in the Babahoyo canton, Los Ríos province, Ecuador.
The values of the sum of probabilities of the sum of effective temperatures
indicate that, in Babahoyo canton, with an intelligent agriculture that integrates
agroclimatic knowledge, it is possible to achieve more efficient and sustainable
productions.
8
Leonardo Santiago Vinces Llaguno
Yaima Trujillo Reyes
Rev. Cient. Interdisciplinaria Investigación y Saberes 11 (2) 2021
1390-8146
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